AGN: the central kiloparsec

SAIt 2008 c

AGN: the central kiloparsec

A highly-biased, idiosyncratic introduction

J.H. Krolik

Department of Physics and Astronomy, Johns Hopkins University, Baltimore MD 21218, USA, e-mail: jhk@jhu.edu

Abstract.

A very personal introduction to the topics of the meeting is presented in which I try to raise the principal questions we would like to answer about every layer in the AGN system, from the edge of the black hole to a kiloparsec out into the host galaxy. Among the topics discussed are: dynamics and thermodynamics of the inner portions of accretion disks; the “natural history” of the broad line region; the structure of the dusty obscuring torus; the growth of black hole mass; and interaction between the AGN and its host galaxy.

1. Introduction

The topics of this meeting cover a very broad range of phenomena within AGN, all the way from the central black hole to the galactic envi- ronment. Because there is a very large contrast in characteristic lengthscale from the event horizon of the black hole to the host galaxy, AGN can be thought of in terms of an “onion skin” model, in which each factor of 10–100 in lengthscale differs qualitatively from the next.

Because, in the end, it is relativistic gravity that rules the roost, the sort of behavior char- acteristic of each layer depends not so much on its absolute distance from the center in cm or pc as on its distance as measured in gravi- tational radii. That is, the fundamental unit of distance most relevant to AGN is

r

≡ GM

c

= 1.47 × 10

M 10

M

cm, (1)

where M is the mass of the central black hole.

Measuring the principal subre- gions of AGN in terms of these units, we may construct a handy table:

Subregion Scale

Inner accretion disk ∼ 10r

Broad line region ∼ 10

–10

r

? Dusty obscuration ∼ 10

r

Warm absorbers ∼ 10

r

? Galactic feedback arena ∼ 10

–10

r

??

As suggested by the question marks, a number of these regions have not yet been well demar- cated empirically; indeed, some would argue that even the distance scales without question marks remain in dispute. Nonetheless, this table indicates the very large dynamic range—

∼ 10

—from the innermost regions relevant to AGN to the outermost.

The remainder of this review will be orga-

nized along the lines of this table, with each of

these regions discussed in turn. For each, I will

briefly summarize some recent work that has

caught my attention, but also, and more impor-

tantly, I will raise some of the questions about

each that we would most like to answer.

turbulence, excited by the magneto-rotational instability, is the fundamental means by which angular momentum is removed from gas and sent outward, permitting matter to sift gradually inward (Balbus & Hawley 1998).

Although entirely intractable to analytic calculation, MHD turbulence can be simulated numerically. The equations defining its evolu- tion are: the familiar Navier-Stokes equations generalized to include magnetic forces, grav- ity, and possibly radiation forces; the mass con- tinuity equation; the Faraday induction equa- tion; and the equation of energy conservation (or at least an equation of state). When neces- sary, these equations can all be written in fully relativistic form without undue complication.

As a set of partial differential equations, they can certainly be messy, but solving multi-term nonlinear equations is just what computers are good for. With large contemporary compute clusters, simulating MHD turbulence in the ac- cretion context is an entirely feasible program.

Certain results have already become well- established. In particular, contrary to the inner disk boundary condition guessed by Novikov & Thorne (1973), magnetic stresses (measured in the fluid frame) do not cease at the innermost stable circular orbit (ISCO); in fact, they persist deep into the plunging region, and, when the black hole spins, continue all the way to the event horizon (Fig. 1: Krolik et al.

(2005)).

Nonetheless, in the present state of the art, not every problem has been solved. There are two principal issues that present difficulties for these simulations: relating dynamics to ther- modynamics and radiation; and the question of whether, and if so, how, dissipation on micro- scopic lengthscales may affect the character of dynamics on much longer lengthscales.

a small segment of the total volume. In disks, the best method for doing so is to restrict at- tention to an annular segment of limited az- imuthal extent. When its radial thickness is small compared to its distance from the cen- ter, and its azimuthal spread is small compared to a radian, it may be “straightened out” into a “shearing box”, a rectangular solid in which the rotational frequency is taken to vary lin- early with radius. Because accretion disks are expected to be very optically thick, it is rea- sonable to solve the radiation transfer problem within such a box in the diffusion approxima- tion, applying a “flux-limiter” only near the top and bottom photospheres to ensure that the flux never exceeds the radiation energy den- sity times c. In addition, energy conservation can be maintained to high accuracy by requir- ing that any magnetic or kinetic energy lost to numerical error be transferred to gas ther- mal energy at every time-step in every cell (Hirose et al. 2006).

With these techniques, a thirty year- old question has now been settled: whether radiation-dominated disks are thermally un- stable (Shakura & Sunyaev 1976). This is an important question because the generic state of the inner regions of all reasonably bright disks around relativistic central objects is one in which radiation dominates gas pres- sure (Shakura & Sunyaev 1973). By “inner re- gions”, one means

r < 170r

m ˙

(M/M

)

, (2) where ˙ m is the accretion rate in Eddington units. Thus, the part of the disk where the great majority of the light output is made should be radiation-dominated whenever the accretion rate is more than a small fraction of Eddington.

The original prediction of thermal insta-

bility for radiation-dominated disks was based

Fig. 1. Shell-integrated electromagnetic fluid-frame stress (solid curve) at an individual moment in simu- lations with a non-rotating black hole (left panel) and one with spin parameter a/M = 0.9 (right panel). In both cases, the dotted curve is the prediction of the Novikov-Thorne model for the time-averaged accretion rate in each of the simulations. Both figures are from Krolik et al. (2005).

on following the α-model—that the stress is always proportional to the total pressure—

to its logical conclusions. In that model, the vertically-integrated dissipation rate is ∼ αp

h, for characteristic radiation pressure p

and ver- tical thickness h. When radiation force is the primary support against the vertical component of gravity, h is proportional to the total radia- tion flux, which, in thermal balance, is identical to the vertically-integrated dissipation rate. So fluctuations in the pressure lead to new heating fluctuations of twice their fractional magnitude and a corresponding amplification of the pres- sure fluctuation.

This all sounds very plausible; it’s just not what disks do when the stress is due to MHD turbulence (see Fig. 2, taken from Hirose et al.

(2008)). When MHD turbulence is the primary motor of the system, its fluctuations control the dissipation rate, and turbulent dissipation gen- erates the heat for radiation pressure, leading to a correlation between magnetic stress and pres- sure. However, there is no discernible back- reaction by which the amplitude of the turbu- lent stress is influenced by the time-dependent magnitude of the pressure; in fact, fluctuations in the magnetic energy lead fluctuations in the radiation energy by about a cooling time.

New efforts are also being made to recal- culate the total radiative efficiency of black hole accretion. Because the classical esti- mate (Novikov & Thorne 1973) depends crit- ically on the no-stress inner boundary condi- tion, the recent findings on magnetic stresses

Fig. 2. Box-integrated radiation energy (blue curve), gas thermal energy (green curve), and mag- netic energy (red curve) as functions of time in one of the two simulations reported by Hirose et al.

(2008). The duration of the simulation, 600 orbits, was more than 40 cooling times.

near the ISCO re-open what had once been thought to be a solved problem. Two meth- ods have been tried so far: estimating dissi- pation from local stresses in purely dynam- ical simulations (Beckwith et al. 2008b), and introducing an optically thin toy-model cool- ing function into dynamical simulations that employ an intrinsically conservative algorithm (Noble, Krolik & Hawley 2008). Both indicate interesting augmentations above the NT num- ber, but the results are still preliminary.

Although these new developments are very

interesting and suggestive, they do not touch

several questions so important that, without an-

Where is it? Why does it receive so much power?

• Roughly ∼ 10% of the AGN population is

“radio-loud” (Jiang et al. 2007), and therefore drives a strong jet. Why do some AGN produce much stronger jets than others? Although black hole spin has long been fingered as the fac- tor most significant to jet strength (Blandford 1990; Wilson & Colbert 1995), the behavior of Galactic black hole binaries demonstrates that spin cannot be the only parameter regulat- ing jet power. Recent simulational work sug- gests that magnetic topology may be a possible second parameter (Beckwith et al. 2008a); are there other factors as well?

3. The Broad Emission and Absorption Line Regions:

r ∼ (10

− 10

)r

Although a topic of immense effort twenty and thirty years ago, this element of the AGN phe- nomenon has received far less attention re- cently. That this should be so reflects not so much the unimportance of the topic as its dif- ficulty. Despite those years of hard work, we still do not know the answers to the most ba- sic questions about this region: What is the broad line region? What is its relation to the accretion flow that powers AGN? Is it part of the disk or separate? Is it a smooth flow or large numbers of individual clouds? What forces—gravity, radiation, gas pressure, mag- netic, . . .—are most important in determining its dynamics? Our understanding of these is- sues has advanced distressingly little since, for example, the review of Osterbrock & Mathews (1986), written more than twenty years ago.

Instead, in recent years AGN broad emis- sion lines have been studied more for their diagnostic power in potentially revealing the

importance of black hole mass distributions in the context of galaxy evolution studies, this question demands a clear answer.

Virtually the same list of questions applies to the broad absorption line region—we know nothing about its place in the grand scheme of AGN. In fact, matters are even worse for the broad absorption line region than for the broad emission line region. Reverberation mapping (and photoionization analysis) provide good measures of the size scale of the broad emis- sion line region, but they provide no help for placing the broad absorption line gas. All we can say with any confidence is that it must lie outside the emission line region because ab- sorption features commonly cut into emission line profiles.

A new development may contribute to con- straining models for emission line gas. A few years ago, Jeremy Goodman argued that AGN disks may not survive fragmentation due to their own gravity beyond ∼ 10

r

from the cen- tral engine (Goodman 2003). If so, it would be very difficult to associate the broad emis- sion line region with a smooth disk outflow.

There may now be a direct observational con-

straint on this question: spectropolarimetry of

six quasars has shown how the characteristic

F

∝ ν

spectrum expected from thermally-

radiating disks extends into the near-IR, reveal-

ing a conventional disk structure out almost

to the radius where fragmentation might hap-

pen (Kishimoto et al. 2008). If these efforts can

be carried to slightly longer wavelengths, we

might be able to observe directly the part of

the disk where either fragmentation or a disk-

associated broad emission line region might

occur.

Fig. 3. Superimposed on an image of the radio continuum (black contours) and the H

O masers (colored spots, radial velocity calibrated as shown in the color bar), the pink oval shows the resolved near-IR emission of the obscuring torus in NGC 1068, and the blue band shows an estimate of the scale of the (over-resolved) longer-wavelength IR (Raban et al. 2008). The beam-size in the near-IR is shown by the small gray oval in the lower-left corner.

4. Dusty obscuration: r ∼ 10

r

Ever since the pioneering work of Antonucci & Miller (1985), we have known that in many (perhaps nearly all) AGN, there is a roughly toroidal belt of very optically thick dusty gas lying somewhere between the broad and narrow emission line regions.

Although its presence can be made evident indirectly through spectropolarimetry (as in Antonucci & Miller (1985)) or through the creation of ionization cones or through its role in forming the infrared continuum, seeing its structure directly has been an elusive goal because its characteristic angular size, even in the closest examples, is only ∼ 10 milli arc-sec. Now that infra-red interferometry is a reality, this region can be directly imaged in at least a small number of especially favorable cases.

NGC 1068 (as always!) is the best exam- ple (Fig. 3: Raban et al. (2008)). Its warmest dust is spread over a region only ' 1.5 pc in diameter, and considerably thinner in the transverse direction. This size is remarkably close to the what was estimated on the ba- sis of its infrared luminosity many years ago (Pier & Krolik 1993). With renewed confi- dence that we have some understanding of the overall geometry of the obscuration, we can

return to the effort to understand its dynam- ics and origin. From the very start, one of the principal questions regarding this gas is how it maintains a geometrically thick profile. Given orbital speeds of hundreds of km/s at its lo- cation, thermal motions capable of support- ing it against the vertical component of grav- ity would be far too rapid to permit any dust to survive (Krolik & Begelman 1988). It is pos- sible that the matter could be strongly enough clumped so as to make collisions (at highly su- personic speeds) relatively rare, but the stir- ring required to support these speeds poses a daunting puzzle(Krolik & Begelman 1988).

Alternatively, this structure might be an ex- ample of a magnetized wind (K¨onigl & Kartje 1994; Elitzur & Shlosman 2006).

One of the few things we know for certain

about dynamics in this gas is that it must feel

a strong radiation force. One way or another,

a large part of the luminosity emitted by the

central engine is reprocessed into the mid-IR

by this matter (as demonstrated by the VLTI

image and the strength and spectrum of the

IR continuum); as this energy passes through

the obscuration, it exerts a force whose associ-

ated acceleration is κF /c, where κ is the opac-

ity per unit mass of the material and F is the

magnitude of the local radiation flux. We know

that this gas is dusty; if the ratio of dust/gas is

(Pier & Krolik 1992). With a few mathemati- cal tricks, it is possible to compute the self- consistent structure of such an infrared radi- ation pressure-supported torus (an example is shown in Fig. 4a: Shi & Krolik (2008)).

Rather than beginning with forces and working toward structure, it is also possi- ble to begin with the spectrum and work backward toward geometry. Elitzur and col- laborators have argued on the basis of ap- proximate inhomogeneous transfer calcula- tions that the comparative weakness of sil- icate features in most Seyfert spectra sug- gests a highly clumped structure (most re- cently in Nenkova et al. (2008)). Interestingly, type 2 quasars sometimes do show strong silicate absorption, suggesting a possible change in internal structure as a function of luminosity (Zakamska et al. 2008). We al- ready have good reason to believe that the solid angle covered by obscuration declines slowly with increasing luminosity (Ueda et al.

2003; Steffen et al. 2003; Barger et al. 2005;

Hao et al. 2005; Treister et al. 2008), so fur- ther structural change dependent on luminos- ity would not be surprising. As genuine 3-d radiation transfer calculations become better able to handle strongly clumped media, more quantitative elucidation of these issues should become possible; a first assay at this prob- lem may be seen in Fig. 4b (Schartmann et al.

2008). If further comparison with spectra pro- vides stronger evidence for clumping, it will then become an interesting challenge to under- stand why the gas is clumped–does it merely reflect how the gas is injected into the torus, or is this a manifestation of some kind of thermal instability?

much easier avenue of counting stellar bulges (Yu & Tremaine 2002). However, the present- day mass function is only the end-product of a process that has lasted the lifetime of the Universe, in which black holes are first formed (by stellar collapse? by direct collapse of gas clouds?) and then grow by some combination of accretion and merger. We would like to know far more about how we arrived where we are.

A concise summary of these events would be contained in the answers to three questions:

• How many seed black holes contribute to a fully-grown black hole in a contemporary galactic nucleus?

• What fraction of all seed black holes end up in a galactic nucleus?

• What fraction of the mass in massive black holes today arrived as a result of accretion, and what fraction in black hole mergers?

“Seed black hole” is used here to denote an ob- ject with a newly-created event horizon.

A complementary set of questions may be asked about the galaxy side of the relationship:

• If AGN “feedback” can regulate star forma- tion in the host, can we see clearer signs of this effect in contemporary, nearby galaxies?

• How does the galaxy regulate the accretion flow into the nucleus? What happens if the galaxy supplies mass at a rate greater than Eddington?

Unfortunately, in the present state of the art, it appears that the only way to attempt to answer these questions is through complicated numerical simulations with literally dozens of free parameters (e.g. Hopkins et al. (2006)).

With these simulations, it is possible to cre-

ate scenarios that appear to be plausible and

reproduce many observable effects, but it re-

mains very difficult to understand which as-

Fig. 4. (Left panel) Logarithmic contours of density in a self-consistent radiation-supported model (Shi & Krolik 2008). The thin white line marks the IR photosphere; the inner boundary is dashed because it is not well-defined in the model. (Right panel) Images of clumpy tori created with varying filling factors (rows from top to bottom are 15%, 30%, 60%) seen from different inclination angles (0

, 60

, 90

from left to right) (Schartmann et al. 2008).

pects of these scenarios are critical to which results, and which results can only be under- stood through the mechanisms employed. The generic problem is that many of the key mech- anisms (e.g., star formation, heating of inter- stellar gas with energy derived from AGN) are treated with phenomenological prescriptions rather than physical ones.

As is so often the case in astrophysics, em- pirical methods may offer the best way for- ward. One such approach that offers hope for quantifying the role of black hole mergers is to detect directly the gravitational waves they generate. Recent advances in numerical relativity (e.g. Pretorius (2005); Baker et al.

(2006); Campanelli et al. (2006)) have given us much greater confidence that we under- stand the strength and form of these waves.

However, the only mission with a hope of de- tecting the gravitational radiation from mas- sive black hole mergers (LISA) is likely 10–

20 years away. In the interim, the best we can hope for is to learn what photon signals might indicate a black hole merger and search for them. There has been much activity in this area in the last few years (Milosavljevic & Phinney 2005; Kocsis et al. 2006; Shields & Bonning 2008; Schnittman & Krolik 2008). The upshot (for the time-being—this is a very rapidly- developing subject) is that if there is enough gas surrounding the merger to generate a sub- stantial luminosity, it will be so optically thick

as to degrade nearly all the light into the infrared. Good-sized mergers may produce quasar-class IR luminosities for ∼ 10

yr; sum- ming over all the mergers in the Universe, ex- isting surveys such as COSMOS may contain a handful of such objects.

Another approach is to explore how the re-

lationship between bulge structure and black

hole mass has evolved over cosmological

timescales. Because we cannot use on distant

galaxies the stellar kinematical techniques that

yield black hole masses in nearby galaxies,

most workers have resorted to estimating the

mass by the line-width method mentioned ear-

lier. Here, however, we run head-on into one of

the questions raised in that context: how trust-

worthy are these estimates? Conceptual ques-

tions about this method were discussed ear-

lier in this review; here we point out that a

number of studies making the assumption that

AGN masses are given by the line-width re-

lation have returned seemingly anomalous re-

sults. For example, Woo et al. (2008) find that

even at redshifts as low as 0.3–0.5, the black

hole masses given by this method are substan-

tially larger than what would have been pre-

dicted on the basis of their host galaxies’ bulge

dispersions and the local correlation. It is hard

to imagine how such a large change in galac-

tic structure could have taken place over such

a short time.

ble for me to attend this meeting.

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